Simplify (-5z^2)^3(4z^3)

Problem

(−5*z^2)^3*(4*z^3)

Solution

1. Apply the power of a product rule to the first term (−5*z^2)^3 by raising both the coefficient and the variable to the third power.

(−5*z^2)^3=(−5)^3⋅(z^2)^3

2. Evaluate the exponent for the constant and apply the power of a power rule (a^m)^n=a^(m*n) to the variable.

(−5)^3=−125

(z^2)^3=z^(2⋅3)=z^6

3. Substitute the simplified term back into the original expression.

−125*z^6⋅4*z^3

4. Multiply the coefficients and apply the product rule for exponents a^m⋅a^n=a^(m+n) to the variables.

−125⋅4=−500

z^6⋅z^3=z^(6+3)=z^9

Final Answer

(−5*z^2)^3*(4*z^3)=−500*z^9

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